Pairing working

src/bn128.js

@@ -0,0 +1,325 @@
+const bigInt = require("big-integer");
+const assert = require("assert");
+
+const F1Field = require("./f1field.js");
+const F2Field = require("./f2field.js");
+const F3Field = require("./f3field.js");
+const GCurve = require("./gcurve.js");
+
+class BN128 {
+
+    constructor() {
+
+        this.q = bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208583");
+        this.r = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
+        this.g1 = [ bigInt(1), bigInt(2) ];
+        this.g2 = [
+            [
+                bigInt("10857046999023057135944570762232829481370756359578518086990519993285655852781"),
+                bigInt("11559732032986387107991004021392285783925812861821192530917403151452391805634")
+            ],
+            [
+                bigInt("8495653923123431417604973247489272438418190587263600148770280649306958101930"),
+                bigInt("4082367875863433681332203403145435568316851327593401208105741076214120093531")
+            ]
+        ];
+
+        this.F1 = new F1Field(this.q);
+        this.F2 = new F2Field(this.F1, bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208582"));
+        this.G1 = new GCurve(this.F1, this.g1);
+        this.G2 = new GCurve(this.F2, this.g2);
+        this.F6 = new F3Field(this.F2, [ bigInt("9"), bigInt("1") ]);
+        this.F12 = new F2Field(this.F6, [ bigInt("9"), bigInt("1") ]);
+        const self = this;
+        this.F12._mulByNonResidue = function(a) {
+            return [self.F2.mul(this.nonResidue, a[2]), a[0], a[1]];
+        };
+
+        this._preparePairing();
+
+    }
+
+    _preparePairing() {
+        this.loopCount = bigInt("29793968203157093288");// CONSTANT
+
+        // Set loopCountNeg
+        if (this.loopCount.isNegative()) {
+            this.loopCount = this.neg();
+            this.loopCountNeg = true;
+        } else {
+            this.loopCountNeg = false;
+        }
+
+        // Set loop_count_bits
+        let lc = this.loopCount;
+        this.loop_count_bits = []; // Constant
+        while (!lc.isZero()) {
+            this.loop_count_bits.push( lc.isOdd() );
+            lc = lc.shiftRight(1);
+        }
+
+        this.two_inv = this.F1.inverse(bigInt(2));
+
+        this.coef_b = bigInt(3);
+        this.twist = [bigInt(9) , bigInt(1)];
+        this.twist_coeff_b = this.F2.mulEscalar(  this.F2.inverse(this.twist), this.coef_b  );
+
+        this.frobenius_coeffs_c1_1 = bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208582");
+        this.twist_mul_by_q_X =
+            [
+                bigInt("21575463638280843010398324269430826099269044274347216827212613867836435027261"),
+                bigInt("10307601595873709700152284273816112264069230130616436755625194854815875713954")
+            ];
+        this.twist_mul_by_q_Y =
+            [
+                bigInt("2821565182194536844548159561693502659359617185244120367078079554186484126554"),
+                bigInt("3505843767911556378687030309984248845540243509899259641013678093033130930403")
+            ];
+
+        this.final_exponent = bigInt("552484233613224096312617126783173147097382103762957654188882734314196910839907541213974502761540629817009608548654680343627701153829446747810907373256841551006201639677726139946029199968412598804882391702273019083653272047566316584365559776493027495458238373902875937659943504873220554161550525926302303331747463515644711876653177129578303191095900909191624817826566688241804408081892785725967931714097716709526092261278071952560171111444072049229123565057483750161460024353346284167282452756217662335528813519139808291170539072125381230815729071544861602750936964829313608137325426383735122175229541155376346436093930287402089517426973178917569713384748081827255472576937471496195752727188261435633271238710131736096299798168852925540549342330775279877006784354801422249722573783561685179618816480037695005515426162362431072245638324744480");
+
+    }
+
+
+    pairing(p1, p2) {
+
+        const pre1 = this.precomputeG1(p1);
+        const pre2 = this.precomputeG2(p2);
+
+        const r1 = this.millerLoop(pre1, pre2);
+
+        const res = this.finalExponentiation(r1);
+
+        return res;
+    }
+
+
+    precomputeG1(p) {
+        const Pcopy = this.G1.affine(p);
+
+        const res = {};
+        res.PX = Pcopy[0];
+        res.PY = Pcopy[1];
+
+        return res;
+    }
+
+    precomputeG2(p) {
+
+        const Qcopy = this.G2.affine(p);
+
+        const res = {
+            QX: Qcopy[0],
+            QY: Qcopy[1],
+            coeffs: []
+        };
+
+        const R = {
+            X: Qcopy[0],
+            Y: Qcopy[1],
+            Z: this.F2.one
+        };
+
+        let c;
+
+        for (let i = this.loop_count_bits.length-2; i >= 0; --i)
+        {
+            const bit = this.loop_count_bits[i];
+
+            c = this._doubleStep(R);
+            res.coeffs.push(c);
+
+            if (bit)
+            {
+                c = this._addStep(Qcopy, R);
+                res.coeffs.push(c);
+            }
+        }
+
+        const Q1 = this.G2.affine(this._g2MulByQ(Qcopy));
+        assert(this.F2.equals(Q1[2], this.F2.one));
+        const Q2 = this.G2.affine(this._g2MulByQ(Q1));
+        assert(this.F2.equals(Q2[2], this.F2.one));
+
+        if (this.loopCountNef)
+        {
+            R.Y = this.F2.neg(R.Y);
+        }
+        Q2[1] = this.F2.neg(Q2[1]);
+
+        c = this._addStep(Q1, R);
+        res.coeffs.push(c);
+
+        c = this._addStep(Q2, R);
+        res.coeffs.push(c);
+
+        return res;
+    }
+
+    millerLoop(pre1, pre2) {
+        let f = this.F12.one;
+
+        let idx = 0;
+
+        let c;
+
+        for (let i = this.loop_count_bits.length-2; i >= 0; --i)
+        {
+            const bit = this.loop_count_bits[i];
+
+            /* code below gets executed for all bits (EXCEPT the MSB itself) of
+               alt_bn128_param_p (skipping leading zeros) in MSB to LSB
+               order */
+
+            c = pre2.coeffs[idx++];
+            f = this.F12.square(f);
+            f = this._mul_by_024(
+                f,
+                c.ell_0,
+                this.F2.mulEscalar(c.ell_VW , pre1.PY),
+                this.F2.mulEscalar(c.ell_VV , pre1.PX, ));
+
+            if (bit)
+            {
+                c = pre2.coeffs[idx++];
+                f = this._mul_by_024(
+                    f,
+                    c.ell_0,
+                    this.F2.mulEscalar(c.ell_VW, pre1.PY, ),
+                    this.F2.mulEscalar(c.ell_VV, pre1.PX, ));
+            }
+
+        }
+
+        if (this.loopCountNef)
+        {
+            f = this.F12.inverse(f);
+        }
+
+        c = pre2.coeffs[idx++];
+        f = this._mul_by_024(
+            f,
+            c.ell_0,
+            this.F2.mulEscalar(c.ell_VW, pre1.PY),
+            this.F2.mulEscalar(c.ell_VV, pre1.PX));
+
+        c = pre2.coeffs[idx++];
+        f = this._mul_by_024(
+            f,
+            c.ell_0,
+            this.F2.mulEscalar(c.ell_VW, pre1.PY, ),
+            this.F2.mulEscalar(c.ell_VV, pre1.PX));
+
+        return f;
+    }
+
+    finalExponentiation(elt) {
+        // TODO: There is an optimization in FF
+
+        const res = this.F12.exp(elt,this.final_exponent);
+
+        return res;
+    }
+
+    _doubleStep(current) {
+        const X = current.X;
+        const Y = current.Y;
+        const Z = current.Z;
+
+        const A = this.F2.mulEscalar(this.F2.mul(X,Y), this.two_inv);                     // A = X1 * Y1 / 2
+        const B = this.F2.square(Y);                           // B = Y1^2
+        const C = this.F2.square(Z);                           // C = Z1^2
+        const D = this.F2.add(C, this.F2.add(C,C));            // D = 3 * C
+        const E = this.F2.mul(this.twist_coeff_b, D);     // E = twist_b * D
+        const F = this.F2.add(E, this.F2.add(E,E));            // F = 3 * E
+        const G =
+            this.F2.mulEscalar(
+                this.F2.add( B , F ),
+                this.two_inv);                            // G = (B+F)/2
+        const H =
+            this.F2.sub(
+                this.F2.square( this.F2.add(Y,Z) ),
+                this.F2.add( B , C));                          // H = (Y1+Z1)^2-(B+C)
+        const I = this.F2.sub(E, B);                           // I = E-B
+        const J = this.F2.square(X);                           // J = X1^2
+        const E_squared = this.F2.square(E);                   // E_squared = E^2
+
+        current.X = this.F2.mul( A, this.F2.sub(B,F) );        // X3 = A * (B-F)
+        current.Y =
+            this.F2.sub(
+                this.F2.sub( this.F2.square(G) , E_squared ),
+                this.F2.add( E_squared , E_squared ));         // Y3 = G^2 - 3*E^2
+        current.Z = this.F2.mul( B, H );                       // Z3 = B * H
+        const c = {
+            ell_0 : this.F2.mul( I, this.twist),          // ell_0 = xi * I
+            ell_VW: this.F2.neg( H ),                          // ell_VW = - H (later: * yP)
+            ell_VV: this.F2.add( J , this.F2.add(J,J) )        // ell_VV = 3*J (later: * xP)
+        };
+
+        return c;
+    }
+
+    _addStep(base, current) {
+
+        const X1 = current.X;
+        const Y1 = current.Y;
+        const Z1 = current.Z;
+        const x2 = base[0];
+        const y2 = base[1];
+
+        const D = this.F2.sub( X1, this.F2.mul(x2,Z1) );  // D = X1 - X2*Z1
+        const E = this.F2.sub( Y1, this.F2.mul(y2,Z1) );  // E = Y1 - Y2*Z1
+        const F = this.F2.square(D);                      // F = D^2
+        const G = this.F2.square(E);                      // G = E^2
+        const H = this.F2.mul(D,F);                       // H = D*F
+        const I = this.F2.mul(X1,F);                      // I = X1 * F
+        const J =
+            this.F2.sub(
+                this.F2.add( H, this.F2.mul(Z1,G) ),
+                this.F2.add( I, I ));                     // J = H + Z1*G - (I+I)
+
+        current.X = this.F2.mul( D , J );                 // X3 = D*J
+        current.Y =
+            this.F2.sub(
+                this.F2.mul( E , this.F2.sub(I,J) ),
+                this.F2.mul( H , Y1));                    // Y3 = E*(I-J)-(H*Y1)
+        current.Z = this.F2.mul(Z1,H);
+        const c = {
+            ell_0 :
+                this.F2.mul(
+                    this.twist,
+                    this.F2.sub(
+                        this.F2.mul(E , x2),
+                        this.F2.mul(D , y2))),            // ell_0 = xi * (E * X2 - D * Y2)
+            ell_VV : this.F2.neg(E),                      // ell_VV = - E (later: * xP)
+            ell_VW : D                                    // ell_VW = D (later: * yP )
+        };
+
+        return c;
+    }
+
+    _mul_by_024(a, ell_0, ell_VW, ell_VV) {
+
+        const b = [
+            [ell_0, this.F2.zero, ell_VV],
+            [this.F2.zero, ell_VW, this.F2.zero]
+        ];
+
+        return this.F12.mul(a,b);
+
+        // TODO There is a better version on libff. It should be ported.
+    }
+
+    _g2MulByQ(p) {
+        const fmx = [p[0][0], this.F1.mul(p[0][1], this.frobenius_coeffs_c1_1 )];
+        const fmy = [p[1][0], this.F1.mul(p[1][1], this.frobenius_coeffs_c1_1 )];
+        const fmz = [p[2][0], this.F1.mul(p[2][1], this.frobenius_coeffs_c1_1 )];
+        return [
+            this.F2.mul(this.twist_mul_by_q_X , fmx),
+            this.F2.mul(this.twist_mul_by_q_Y , fmy),
+            fmz
+        ];
+    }
+}
+
+module.exports = BN128;

src/constants.js

@@ -24,8 +24,10 @@ const C = {
             ]
         ],
 
-    f2nonResidue: bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208582")
-
+    f2nonResidue: bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208582"),
+    f6nonResidue: [ bigInt("9"), bigInt("1") ],
+    f12nonResidue: [
+    ]
 };
 
 const F1 = new F1Field(C.q);
@@ -35,7 +37,8 @@ C.two_inv= F1.inverse(bigInt(2));
 
 C.coef_b = bigInt(3);
 C.twist = [bigInt(9) , bigInt(1)];
-// C.twist_coeff_b = F2.mulEscalar(  F2.inverse(C.twist), C.coef_b  );
+C.twist_coeff_b = F2.mulEscalar(  F2.inverse(C.twist), C.coef_b  );
 
 
 module.exports = C;
+

src/f12field.js

@@ -1,55 +0,0 @@
-
-
-
-class F12Field {
-    constructor(p) {
-        this.p = n;
-    }
-
-    add(a, b) {
-        const maxGrade = Math.max(a.length, b.length);
-        const res = new Array(maxGrade);
-        for (let i=0; i<maxGrade; i++) {
-            res[i] = this.F.add(a[i], b[i]);
-        }
-        return this._reduce(res);
-    }
-
-    sub(a, b) {
-        // TODO
-        throw new Error("Not Implementted");
-    }
-
-    neg(a) {
-        // TODO
-        throw new Error("Not Implementted");
-    }
-
-    mul(a, b) {
-        // TODO
-        throw new Error("Not Implementted");
-    }
-
-    inverse(a, b) {
-        // TODO
-        throw new Error("Not Implementted");
-    }
-
-    div(a, b) {
-        // TODO
-        throw new Error("Not Implementted");
-    }
-
-    isZero(a) {
-        // TODO
-        throw new Error("Not Implementted");
-    }
-
-    mul_by_024(a, ell0, ellVW, ellVV) {
-        // TODO
-        throw new Error("Not Implementted");
-    }
-
-}
-
-module.exports = F2Field;

src/f1field.js

@@ -1,4 +1,5 @@
 const bigInt = require("big-integer");
+const fUtils = require("./futils.js");
 
 class F1Field {
     constructor(q) {
@@ -8,10 +9,6 @@ class F1Field {
         this.one = bigInt.one;
     }
 
-    e(a) {
-        return bigInt(a);
-    }
-
     copy(a) {
         return bigInt(a);
     }
@@ -20,6 +17,10 @@ class F1Field {
         return a.add(b);
     }
 
+    double(a) {
+        return this.add(a,a);
+    }
+
     sub(a, b) {
         return a.minus(b);
     }
@@ -69,6 +70,14 @@ class F1Field {
         return aux;
     }
 
+    mulEscalar(base, e) {
+        return fUtils.mulEscalar(this, base, e);
+    }
+
+    exp(base, e) {
+        return fUtils.exp(this, base, e);
+    }
+
     toString(a) {
         const ca = this.affine(a);
         return `"0x${ca.toString(16)}"`;

src/f2field.js

@@ -1,4 +1,4 @@
-const bigInt = require("big-integer");
+const fUtils = require("./futils.js");
 
 class F2Field {
     constructor(F, nonResidue) {
@@ -8,8 +8,8 @@ class F2Field {
         this.nonResidue = nonResidue;
     }
 
-    e(c0, c1) {
-        return [bigInt(c0), bigInt(c1)];
+    _mulByNonResidue(a) {
+        return this.F.mul(this.nonResidue, a);
     }
 
     copy(a) {
@@ -23,6 +23,10 @@ class F2Field {
         ];
     }
 
+    double(a) {
+        return this.add(a,a);
+    }
+
     sub(a, b) {
         return [
             this.F.sub(a[0], b[0]),
@@ -39,7 +43,7 @@ class F2Field {
         const bB = this.F.mul(a[1] , b[1]);
 
         return [
-            this.F.add( aA , this.F.mul(this.nonResidue , bB)),
+            this.F.add( aA , this._mulByNonResidue(bB)),
             this.F.sub(
                 this.F.mul(
                     this.F.add(a[0], a[1]),
@@ -50,7 +54,7 @@ class F2Field {
     inverse(a) {
         const t0 = this.F.square(a[0]);
         const t1 = this.F.square(a[1]);
-        const t2 = this.F.sub(t0, this.F.mul(this.nonResidue, t1));
+        const t2 = this.F.sub(t0, this._mulByNonResidue(t1));
         const t3 = this.F.inverse(t2);
         return [
             this.F.mul(a[0], t3),
@@ -77,10 +81,10 @@ class F2Field {
                     this.F.add(a[0], a[1]) ,
                     this.F.add(
                         a[0] ,
-                        this.F.mul(this.nonResidue , a[1]))),
+                        this._mulByNonResidue(a[1]))),
                 this.F.add(
                     ab,
-                    this.F.mul(this.nonResidue, ab))),
+                    this._mulByNonResidue(ab))),
             this.F.add(ab, ab)
         ];
     }
@@ -97,6 +101,14 @@ class F2Field {
         return [this.F.affine(a[0]), this.F.affine(a[1])];
     }
 
+    mulEscalar(base, e) {
+        return fUtils.mulEscalar(this, base, e);
+    }
+
+    exp(base, e) {
+        return fUtils.exp(this, base, e);
+    }
+
     toString(a) {
         const cp = this.affine(a);
         return `[ ${this.F.toString(cp[0])} , ${this.F.toString(cp[1])} ]`;

src/f3field.js

@@ -0,0 +1,158 @@
+const fUtils = require("./futils.js");
+
+class F3Field {
+    constructor(F, nonResidue) {
+        this.F = F;
+        this.zero = [this.F.zero, this.F.zero, this.F.zero];
+        this.one = [this.F.one, this.F.zero, this.F.zero];
+        this.nonResidue = nonResidue;
+    }
+
+    _mulByNonResidue(a) {
+        return this.F.mul(this.nonResidue, a);
+    }
+
+    copy(a) {
+        return [this.F.copy(a[0]), this.F.copy(a[1]), this.F.copy(a[2])];
+    }
+
+    add(a, b) {
+        return [
+            this.F.add(a[0], b[0]),
+            this.F.add(a[1], b[1]),
+            this.F.add(a[2], b[2])
+        ];
+    }
+
+    double(a) {
+        return this.add(a,a);
+    }
+
+    sub(a, b) {
+        return [
+            this.F.sub(a[0], b[0]),
+            this.F.sub(a[1], b[1]),
+            this.F.sub(a[2], b[2])
+        ];
+    }
+
+    neg(a) {
+        return this.sub(this.zero, a);
+    }
+
+    mul(a, b) {
+
+        const aA = this.F.mul(a[0] , b[0]);
+        const bB = this.F.mul(a[1] , b[1]);
+        const cC = this.F.mul(a[2] , b[2]);
+
+        return [
+            this.F.add(
+                aA,
+                this._mulByNonResidue(
+                    this.F.sub(
+                        this.F.mul(
+                            this.F.add(a[1], a[2]),
+                            this.F.add(b[1], b[2])),
+                        this.F.add(bB, cC)))),    // aA + non_residue*((b+c)*(B+C)-bB-cC),
+
+            this.F.add(
+                this.F.sub(
+                    this.F.mul(
+                        this.F.add(a[0], a[1]),
+                        this.F.add(b[0], b[1])),
+                    this.F.add(aA, bB)),
+                this._mulByNonResidue( cC)),   // (a+b)*(A+B)-aA-bB+non_residue*cC
+
+            this.F.add(
+                this.F.sub(
+                    this.F.mul(
+                        this.F.add(a[0], a[2]),
+                        this.F.add(b[0], b[2])),
+                    this.F.add(aA, cC)),
+                bB)];                           // (a+c)*(A+C)-aA+bB-cC)
+    }
+
+    inverse(a) {
+        const t0 = this.F.square(a[0]);             // t0 = a^2 ;
+        const t1 = this.F.square(a[1]);             // t1 = b^2 ;
+        const t2 = this.F.square(a[2]);             // t2 = c^2;
+        const t3 = this.F.mul(a[0],a[1]);           // t3 = ab
+        const t4 = this.F.mul(a[0],a[2]);           // t4 = ac
+        const t5 = this.F.mul(a[1],a[2]);           // t5 = bc;
+        // c0 = t0 - non_residue * t5;
+        const c0 = this.F.sub(t0, this._mulByNonResidue(t5));
+        // c1 = non_residue * t2 - t3;
+        const c1 = this.F.sub(this._mulByNonResidue(t2), t3);
+        const c2 = this.F.sub(t1, t4);              // c2 = t1-t4
+
+        // t6 = (a * c0 + non_residue * (c * c1 + b * c2)).inverse();
+        const t6 =
+            this.F.inverse(
+                this.F.add(
+                    this.F.mul(a[0], c0),
+                    this._mulByNonResidue(
+                        this.F.add(
+                            this.F.mul(a[2], c1),
+                            this.F.mul(a[1], c2)))));
+
+        return [
+            this.F.mul(t6, c0),         // t6*c0
+            this.F.mul(t6, c1),         // t6*c1
+            this.F.mul(t6, c2)];        // t6*c2
+    }
+
+    div(a, b) {
+        return this.mul(a, this.inverse(b));
+    }
+
+    square(a) {
+        const s0 = this.F.square(a[0]);                   // s0 = a^2
+        const ab = this.F.mul(a[0], a[1]);                // ab = a*b
+        const s1 = this.F.add(ab, ab);                    // s1 = 2ab;
+        const s2 = this.F.square(
+            this.F.add(this.F.sub(a[0],a[1]), a[2]));     // s2 = (a - b + c)^2;
+        const bc = this.F.mul(a[1],a[2]);                 // bc = b*c
+        const s3 = this.F.add(bc, bc);                    // s3 = 2*bc
+        const s4 = this.F.square(a[2]);                   // s4 = c^2
+
+
+        return [
+            this.F.add(
+                s0,
+                this._mulByNonResidue(s3)),           // s0 + non_residue * s3,
+            this.F.add(
+                s1,
+                this._mulByNonResidue(s4)),           // s1 + non_residue * s4,
+            this.F.sub(
+                this.F.add( this.F.add(s1, s2) , s3 ),
+                this.F.add(s0, s4))];                      // s1 + s2 + s3 - s0 - s4
+    }
+
+    isZero(a) {
+        return this.F.isZero(a[0]) && this.F.isZero(a[1]) && this.F.isZero(a[2]);
+    }
+
+    equals(a, b) {
+        return this.F.equals(a[0], b[0]) && this.F.equals(a[1], b[1]) && this.F.equals(a[2], b[2]);
+    }
+
+    affine(a) {
+        return [this.F.affine(a[0]), this.F.affine(a[1]), this.F.affine(a[2])];
+    }
+
+    mulEscalar(base, e) {
+        return fUtils.mulEscalar(this, base, e);
+    }
+
+    exp(base, e) {
+        return fUtils.exp(this, base, e);
+    }
+
+    toString(a) {
+        const cp = this.affine(a);
+        return `[ ${this.F.toString(cp[0])} , ${this.F.toString(cp[1])}, ${this.F.toString(cp[2])} ]`;
+    }
+}
+
+module.exports = F3Field;

src/futils.js

@@ -0,0 +1,34 @@
+const bigInt = require("big-integer");
+
+exports.mulEscalar = (F, base, e) =>{
+    let res = F.zero;
+    let rem = bigInt(e);
+    let exp = base;
+
+    while (! rem.isZero()) {
+        if (rem.isOdd()) {
+            res = F.add(res, exp);
+        }
+        exp = F.double(exp);
+        rem = rem.shiftRight(1);
+    }
+
+    return res;
+};
+
+
+exports.exp = (F, base, e) =>{
+    let res = F.one;
+    let rem = bigInt(e);
+    let exp = base;
+
+    while (! rem.isZero()) {
+        if (rem.isOdd()) {
+            res = F.mul(res, exp);
+        }
+        exp = F.square(exp);
+        rem = rem.shiftRight(1);
+    }
+
+    return res;
+};

src/gcurve.js

@@ -1,3 +1,4 @@
+const fUtils = require("./futils.js");
 
 class GCurve {
 
@@ -105,19 +106,7 @@ class GCurve {
     }
 
     mulEscalar(base, e) {
-        let res = this.zero;
-        let rem = e;
-        let exp = base;
-
-        while (! rem.isZero()) {
-            if (rem.isOdd()) {
-                res = this.add(res, exp);
-            }
-            exp = this.double(exp);
-            rem = rem.shiftRight(1);
-        }
-
-        return res;
+        return fUtils.mulEscalar(this, base, e);
     }
 
     affine(p) {

src/gt.js

@@ -1,20 +0,0 @@
-const bigInt = require("big-integer");
-const ZnField = require("./znfield.js");
-
-module.eports = class Gt {
-
-    constructor() {
-        // TODO
-        throw new Error("Not Implementted");
-    }
-
-    mul(p1, p2) {
-        // TODO
-        throw new Error("Not Implementted");
-    }
-
-    equal(p1, p2) {
-        // TODO
-        throw new Error("Not Implementted");
-    }
-};

src/pairing.js

@@ -4,11 +4,10 @@ This module calculate the pairing of p1 and p2 where p1 in G1 and p2 in G2
 
 const assert = require("assert");
 const bigInt = require("big-integer");
-const F1Field = require("f1field");
-const F2Field = require("f2field");
-const F12Field = require("f12field");
-const G1Curve = require("g1curve");
-const G2Curve = require("g2curve");
+const F1Field = require("./f1field");
+const F2Field = require("./f2field");
+const F3Field = require("./f3field");
+const GCurve = require("./gcurve");
 const constants = require("constants");
 
 module.exports = new Pairing();
@@ -16,8 +15,8 @@ module.exports = new Pairing();
 
 class Pairing {
 
-    constructor() {
-        this.loopCount = bigInt(11);// CONSTANT
+    constructor(curve) {
+        this.loopCount = bigInt("29793968203157093288");// CONSTANT
 
         // Set loopCountNeg
         if (this.loopCount.isNegative()) {
@@ -30,18 +29,17 @@ class Pairing {
         // Set loop_count_bits
         let lc = this.loopCount;
         this.loop_count_bits = []; // Constant
-        while (lc) {
+        while (!lc.isZero()) {
             this.loop_count_bits.push( lc.isOdd() );
             lc = lc.shiftRight(1);
         }
 
-        this.F12 = new F12Field(constants.q);
-        this.F2 = new F2Field(constants.q);
-        this.F1 = new F1Field(constants.q);
-        this.G1 = new GCurve(F1, constants.g1);
-        this.G2 = new GCurve(F2, constants.g2);
-
-        this.twoInv = this.F1.inverse(bigInt(2));
+        this.F1 = curve.F1;
+        this.F2 = curve.F2;
+        this.G1 = curve.G1;
+        this.G2 = curve.G2;
+        this.F6 = curve.F6;
+        this.F12 = curve.F12;
     }
 
     pairing(p1, p2) {
@@ -134,7 +132,7 @@ class Pairing {
 
             c = pre2.coeffs[idx++];
             f = this.F12.square(f);
-            f = this.F12.mul_by_024(
+            f = this._mul_by_024(
                 f,
                 c.ell_0,
                 this.F2.mul(pre1.PY, c.ell_VW),
@@ -143,7 +141,7 @@ class Pairing {
             if (bit)
             {
                 c = pre2.coeffs[idx++];
-                f = this.F12.mul_by_024(
+                f = this._mul_by_024(
                     f,
                     c.ell_0,
                     this.F2.mul(pre1.PY, c.ell_VW),
@@ -158,14 +156,14 @@ class Pairing {
         }
 
         c = pre2.coeffs[idx++];
-        f = this.F12.mul_by_024(
+        f = this._mul_by_024(
             f,
             c.ell_0,
             this.F2.mul(pre1.PY, c.ell_VW),
             this.F2.mul(pre1.PX, c.ell_VV));
 
         c = pre2.coeffs[idx++];
-        f = this.F12.mul_by_024(
+        f = this._mul_by_024(
             f,
             c.ell_0,
             this.F2.mul(pre1.PY, c.ell_VW),
@@ -250,4 +248,16 @@ class Pairing {
 
         return c;
     }
+
+    _mul_by_024(a, ell_0, ell_VW, ell_VV) {
+
+        const b = [
+            [ell_0, this.F2.zero, ell_VV],
+            [this.F2.zero, ell_VW, this.F2.zero]
+        ];
+
+        return this.F12.mul(a,b);
+
+        // TODO There is a better version on libff. It should be ported.
+    }
 }

test/algebra.js

@@ -1,72 +1,151 @@
-const bigInt = require("big-integer");
-const F1Field = require("../src/f1field.js");
-const F2Field = require("../src/f2field.js");
-const GCurve = require("../src/gcurve.js");
-const constants = require("../src/constants.js");
 const chai = require("chai");
 
+const bigInt = require("big-integer");
+const BN128 = require("../src/BN128.js");
+
 const assert = chai.assert;
 
 describe("Curve G1 Test", () => {
-    it ("r*one == 0", () => {
-        const F1 = new F1Field(constants.q);
-        const G1 = new GCurve(F1, constants.g1);
+    it("r*one == 0", () => {
+        const bn128 = new BN128();
 
-        const res = G1.mulEscalar(G1.g, constants.r);
+        const res = bn128.G1.mulEscalar(bn128.G1.g, bn128.r);
 
-        assert(G1.equals(res, G1.zero), "G1 does not have range r");
+        assert(bn128.G1.equals(res, bn128.G1.zero), "G1 does not have range r");
     });
 
     it("Should add match in various in G1", () => {
-        const F1 = new F1Field(constants.q);
-        const G1 = new GCurve(F1, constants.g1);
+
+        const bn128 = new BN128();
 
         const r1 = bigInt(33);
         const r2 = bigInt(44);
 
-        const gr1 = G1.mulEscalar(G1.g, r1);
-        const gr2 = G1.mulEscalar(G1.g, r2);
+        const gr1 = bn128.G1.mulEscalar(bn128.G1.g, r1);
+        const gr2 = bn128.G1.mulEscalar(bn128.G1.g, r2);
 
-        const grsum1 = G1.add(gr1, gr2);
+        const grsum1 = bn128.G1.add(gr1, gr2);
 
-        const grsum2 = G1.mulEscalar(G1.g, r1.add(r2));
+        const grsum2 = bn128.G1.mulEscalar(bn128.G1.g, r1.add(r2));
 
-        assert(G1.equals(grsum1, grsum2));
+        assert(bn128.G1.equals(grsum1, grsum2));
     });
 });
 
 describe("Curve G2 Test", () => {
     it ("r*one == 0", () => {
-        const F1 = new F1Field(constants.q);
-        const F2 = new F2Field(F1, constants.f2nonResidue);
-        const G2 = new GCurve(F2, constants.g2);
+        const bn128 = new BN128();
 
-        const res = G2.mulEscalar(G2.g, constants.r);
+        const res = bn128.G2.mulEscalar(bn128.G2.g, bn128.r);
 
-        assert(G2.equals(res, G2.zero), "G2 does not have range r");
+        assert(bn128.G2.equals(res, bn128.G2.zero), "G2 does not have range r");
     });
 
     it("Should add match in various in G2", () => {
-        const F1 = new F1Field(constants.q);
-        const F2 = new F2Field(F1, constants.f2nonResidue);
-        const G2 = new GCurve(F2, constants.g2);
+        const bn128 = new BN128();
 
         const r1 = bigInt(33);
         const r2 = bigInt(44);
 
-        const gr1 = G2.mulEscalar(G2.g, r1);
-        const gr2 = G2.mulEscalar(G2.g, r2);
+        const gr1 = bn128.G2.mulEscalar(bn128.G2.g, r1);
+        const gr2 = bn128.G2.mulEscalar(bn128.G2.g, r2);
 
-        const grsum1 = G2.add(gr1, gr2);
+        const grsum1 = bn128.G2.add(gr1, gr2);
 
-        const grsum2 = G2.mulEscalar(G2.g, r1.add(r2));
+        const grsum2 = bn128.G2.mulEscalar(bn128.G2.g, r1.add(r2));
 
         /*
         console.log(G2.toString(grsum1));
         console.log(G2.toString(grsum2));
         */
 
-        assert(G2.equals(grsum1, grsum2));
+        assert(bn128.G2.equals(grsum1, grsum2));
+    });
+});
+
+describe("F6 testing", () => {
+    it("Should multiply and divide in F6", () => {
+        const bn128 = new BN128();
+        const a =
+            [
+                [bigInt("1"), bigInt("2")],
+                [bigInt("3"), bigInt("4")],
+                [bigInt("5"), bigInt("6")]
+            ];
+        const b =
+            [
+                [bigInt("12"), bigInt("11")],
+                [bigInt("10"), bigInt("9")],
+                [bigInt("8"), bigInt("7")]
+            ];
+        const c = bn128.F6.mul(a,b);
+        const d = bn128.F6.div(c,b);
+
+        assert(bn128.F6.equals(a, d));
+    });
+});
+
+describe("F12 testing", () => {
+    it("Should multiply and divide in F12", () => {
+        const bn128 = new BN128();
+        const a =
+        [
+            [
+                [bigInt("1"), bigInt("2")],
+                [bigInt("3"), bigInt("4")],
+                [bigInt("5"), bigInt("6")]
+            ],
+            [
+                [bigInt("7"), bigInt("8")],
+                [bigInt("9"), bigInt("10")],
+                [bigInt("11"), bigInt("12")]
+            ]
+        ];
+        const b =
+        [
+            [
+                [bigInt("12"), bigInt("11")],
+                [bigInt("10"), bigInt("9")],
+                [bigInt("8"), bigInt("7")]
+            ],
+            [
+                [bigInt("6"), bigInt("5")],
+                [bigInt("4"), bigInt("3")],
+                [bigInt("2"), bigInt("1")]
+            ]
+        ];
+        const c = bn128.F12.mul(a,b);
+        const d = bn128.F12.div(c,b);
+
+        assert(bn128.F12.equals(a, d));
     });
+});
+
+describe("Pairing", () => {
+    it("Should match pairing", () => {
+        const bn128 = new BN128();
+
+
+        const g1a = bn128.G1.mulEscalar(bn128.G1.g, 25);
+        const g2a = bn128.G2.mulEscalar(bn128.G2.g, 30);
+
+        const g1b = bn128.G1.mulEscalar(bn128.G1.g, 30);
+        const g2b = bn128.G2.mulEscalar(bn128.G2.g, 25);
+
+
+        const pre1a = bn128.precomputeG1(g1a);
+        const pre2a = bn128.precomputeG2(g2a);
+        const pre1b = bn128.precomputeG1(g1b);
+        const pre2b = bn128.precomputeG2(g2b);
+
+        const r1 = bn128.millerLoop(pre1a, pre2a);
+        const r2 = bn128.millerLoop(pre1b, pre2b);
+
+        const rbe = bn128.F12.mul(r1, bn128.F12.inverse(r2));
+
+        const res = bn128.finalExponentiation(rbe);
+
+        assert(bn128.F12.equals(res, bn128.F12.one));
+    }).timeout(10000);
 
 });